Integrability and Conformal Blocks for Surface Defects in $\mathcal{N}=4$ SYM

Abstract

We study various aspects of half-BPS surface defect operators in $\mathcal{N}=4$ SYM. For defects on generic points on the moduli space we use superconformal symmetry to fix the form of one-point and two-point functions of half-BPS operators and solve the superconformal Ward identities in terms of superconformal blocks, emphasizing the role of the broken rotational symmetry transverse to the defect in the superconformal block expansion. We verify this expansion by the leading-order perturbative calculation for the two-point functions. We also investigate the integrability of the defect CFT in the planar limit and argue that the integrability is broken at generic points of the defect moduli. The integrability is expected to be restored in the singular point of this moduli space where another "rigid" branch appears, and we provide evidence for this by showing that the defect one-point functions in this case can be mapped to a class of known integrable quenches.

51 pages, 7 figures

References in corpus (53)

• N=6 superconformal Chern-Simons-matter theories, M2-branes and their gravity duals
• The Bethe-Ansatz for N=4 Super Yang-Mills
• Review of AdS/CFT Integrability: An Overview
• Hidden Symmetries of the AdS_5 x S^5 Superstring
• Bubbling AdS space and 1/2 BPS geometries
• Infinite Chiral Symmetry in Four Dimensions
• Rigid Supersymmetric Theories in Curved Superspace
• Real-time response in AdS/CFT with application to spinors
• The Bethe ansatz for superconformal Chern-Simons
• What is an integrable quench?
• The Analytic Bethe Ansatz for a Chain with Centrally Extended su(2|2) Symmetry
• 2d Index and Surface operators
• One-point Functions in Defect CFT and Integrability
• Semiclassics, Goldstone Bosons and CFT data
• Bootstrap equations for $\mathcal{N}=4$ SYM with defects
• Integrable open spin chains from giant gravitons
• One-point Functions in AdS/dCFT from Matrix Product States
• A non-renormalization theorem for chiral primary 3-point functions
• Integrable Spin Chain in Superconformal Chern-Simons Theory
• Reflecting magnons
• On Four-Point Functions of Half-BPS Operators in General Dimensions
• Probing N=4 SYM With Surface Operators
• Surface Defects and Resolvents
• Scalar one-point functions and matrix product states of AdS/dCFT
• A study of open strings ending on giant gravitons, spin chains and integrability
• Bubbling Surface Operators And S-Duality
• Conformal field theories in anti-de Sitter space
• More Exact Results in the Wilson Loop Defect CFT: Bulk-Defect OPE, Nonplanar Corrections and Quantum Spectral Curve
• Integrable Open Spin Chains in Defect Conformal Field Theory
• Superconformal surfaces in four dimensions
• Spin Chain Overlaps and the Twisted Yangian
• Integrability of Green-Schwarz Sigma Models with Boundaries
• Classical Open String Integrability
• Integrable Matrix Product States from boundary integrability
• Integrable Open Spin Chain in Super Yang-Mills and the Plane-wave/SYM duality
• A Quantum Check of AdS/dCFT
• Two-point functions in AdS/dCFT and the boundary conformal bootstrap equations
• Taming Defects in $\mathcal{N}=4$ Super-Yang-Mills
• Spinor Exchange in AdS_{d+1}
• Reflecting magnons from D7 and D5 branes
• One-Point Functions of Non-protected Operators in the SO(5) symmetric D3-D7 dCFT
• Supersymmetric Multi-trace Boundary Conditions in AdS
• On factorized overlaps: Algebraic Bethe Ansatz, twists, and Separation of Variables
• On correlation functions of BPS operators in $3d$ $\mathcal{N}=6$ superconformal theories
• Integrable domain walls in ABJM theory
• Crosscap States in Integrable Field Theories and Spin Chains
• A Quantum Check of Non-Supersymmetric AdS/dCFT
• A Unified and Complete Construction of All Finite Dimensional Irreducible Representations of gl(2|2)
• String integrability of defect CFT and dynamical reflection matrices
• Integrable achiral D5-brane reflections and asymptotic Bethe equations
• On the spectral problem of N=4 SYM with orthogonal or symplectic gauge group
• Wilson-loop One-point Functions in ABJM Theory
• A Quantum Framework for AdS/dCFT through Fuzzy Spherical Harmonics on $S^4$

Cited by in corpus (1)

• $\kappa$-symmetric M5 brane web for defects in $Ad{S}_7/CF{T}_6$ holography